1. EXAMPLE 1 Graph a system of two inequalities Graph the system of inequalities. y > –2x – 5 Inequality 1 y < x + 3 Inequality 2

2. EXAMPLE 1 Graph a system of two inequalities STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. SOLUTION STEP 1 Graph each inequality in the system. Use red for y > –2x – 5 and blue for y ≤ x + 3.

3. EXAMPLE 2 Graph a system with no solution Graph the system of inequalities. 2x + 3y < 6 Inequality 1 y < – x + 4 2 3 Inequality 2

4. EXAMPLE 2 Graph a system with no solution STEP 2 Identify the region that is common to both graphs. There is no region shaded both red and blue. So, the system has no solution. SOLUTION STEP 1 2 3 Graph each inequality in the system. Use red for 2x + 3y – x + 4.

5. EXAMPLE 3 Graph a system with an absolute value inequality Graph the system of inequalities. y < 3 Inequality 1 y > x + 4 Inequality 2

6. EXAMPLE 3 Graph a system with an absolute value inequality STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. SOLUTION STEP 1 Graph each inequality in the system. Use red for y ≤ 3 and blue for y > x + 4.

7. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the system of inequalities. 1. y < 3x – 2 y > – x + 4

8. GUIDED PRACTICE for Examples 1, 2 and 3 2. 2x – y > 4 1 2 4x – y < 5

9. GUIDED PRACTICE for Examples 1, 2 and 3 3. x + y > – 3 –6x + y < 1

10. GUIDED PRACTICE for Examples 1, 2 and 3 4. y < 4 y > x – 5

11. GUIDED PRACTICE for Examples 1, 2 and 3 5. y > – 2 y < – x + 2

12. GUIDED PRACTICE for Examples 1, 2 and 3 6. y > 2 x + 1 y < x + 1 This has no solution.